Fu Qidong, Wang Peng, Kartashov Yaroslav V, Konotop Vladimir V, Ye Fangwei
School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China.
Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow Region 108840, Russia.
Phys Rev Lett. 2022 Apr 15;128(15):154101. doi: 10.1103/PhysRevLett.128.154101.
One-dimensional topological pumping of matter waves in two overlaid optical lattices moving with respect to each other is considered in the presence of attractive nonlinearity. It is shown that there exists a threshold nonlinearity level above which the matter transfer is completely arrested. Below this threshold, the transfer of both dispersive wave packets and solitons occurs in accordance with the predictions of the linear theory; i.e., it is quantized and determined by the linear dynamical Chern numbers of the lowest bands. The breakdown of the transport is also explained by nontrivial topology of the bands. In that case, the nonlinearity induces Rabi oscillations of atoms between two (or more) lowest bands. If the sum of the dynamical Chern numbers of the populated bands is zero, the oscillatory dynamics of a matter soliton in space occurs, which corresponds to the transport breakdown. Otherwise, the sum of the Chern numbers of the nonlinearity-excited bands determines the direction and magnitude of the average velocity of matter solitons that remain quantized and admit fractional values. Thus, even in the strongly nonlinear regime the topology of the linear bands is responsible for the evolution of solitons. The transition between different dynamical regimes is accurately described by the perturbation theory for solitons.
在存在吸引性非线性的情况下，考虑了在两个相对运动的叠加光学晶格中物质波的一维拓扑泵浦。结果表明，存在一个阈值非线性水平，高于该水平时物质转移完全停止。低于此阈值时，色散波包和孤子的转移均按照线性理论的预测发生；即，它是量子化的，并由最低能带的线性动力学陈数决定。输运的崩溃也由能带的非平凡拓扑结构来解释。在这种情况下，非线性会诱导原子在两个（或更多）最低能带之间的拉比振荡。如果占据能带的动力学陈数之和为零，则会出现物质孤子在空间中的振荡动力学，这对应于输运崩溃。否则，非线性激发能带的陈数之和决定了仍然量子化且允许分数值的物质孤子平均速度的方向和大小。因此，即使在强非线性区域，线性能带的拓扑结构也决定了孤子的演化。不同动力学区域之间的转变可以通过孤子的微扰理论精确描述。
